Perhaps I'm too tired but is there a problem with the edge weighting
scheme in this algorithim? Consider the following graph:

 __________________
 |                               |
 1___2_______3_____4
     |\               |
     | \________5
     |                |
     |_________6

formula for weight (phi) of edge vw:
if frond (i.e. w<v)                         phi = 2 * w
otherwise if LOWPT2 = v             phi = 2 * LOWPT1
otherwise if LOWPT2 < v             phi = 2 * LOWPT1 + 1

so the edges have the following weights:
phi = 2     (1,2) (2,3) (3,4) (4,1)
phi = 4     (3,5) (5,2) (5,6) (6,2)

The first path (the cycle) is obviously 1,2,3,4,1
But how about the second and third paths? 3,5,2 then 5,6,2  or  3,5,6,2
then 5,2 ?


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